MAT 615: Topics in Algebraic Geometry

Announcements

Welcome to the course!
On February 7, I will be late for my office hours.

About the course

The topic this semester is abelian varieties. We'll discuss the general theory, both from the analytic and algebraic point of view. I also plan to talk about derived categorys of abelian varieties, and about Deligne's theorem on absolute Hodge classes.

Time and location

We meet on Tuesday and Thursday, 11:00am–12:20 pm, in room Physics P–127.

Office hours

My office hours are Friday, 9:30–12:30am.

Lecture notes

The topics covered in each class will appear below. Click on a link to download the notes for that particular class.

Week	Dates	Topic
1	January 28	Lemniscate, doubly periodic functions, elliptic curves
	January 30	Compact complex Lie groups, compact complex tori
2	February 4	Holomorphic line bundles, Appel-Humbert theorem
	February 6	Sections of holomorphic line bundles
3	February 11	Polarizations, Jacobians, morphisms
	February 13	Translations, Lefschetz theorem
4	February 18	Principally polarized abelian varieties, isogenies, Poincaré theorem
	February 20	Abelian varieties, rigidity theorem
5	February 25	Cohomology and base change, Seesaw theorem
	February 27	Theorem of the cube
6	March 4	Theorem of the square, K(L) and ampleness
	March 6	Torsion points, supersingular elliptic curves, quotients by finite groups
7	March 11	The dual abelian variety (in characteristic zero)
	March 13	Properties of the dual abelian variety, seesaw theorem for schemes
8	March 25	Group schemes, the dual abelian variety, cohomology of the structure sheaf
	March 27	Derived categories, derived functors
9	April 1	Grothendieck duality, Mukai's Fourier transform